Simulation of Infinitely Divisible Random Fields

Abstract

Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective integrals. Error bounds for the approximation error are derived and the approximations are used to simulate certain classes of infinitely divisible random fields.

Keywords:

• Approximation
• Infinitely divisible law
• Random field
• Simulation

2000 Mathematics Subject Classification:

• 60G60

Acknowledgments

The authors wish to thank Prof. Urban for his assistance in wavelet-related questions. They also want to thank Generali Versicherung AG, Vienna, Austria, for the kind support of this research.